"...for many reasons we have decided not to register our 'cultural' marriage, so I'm still a Miss."
and
"Is it easier just to register our marriage so it's recognised in the UK?"
It depends where you got married.
If you had a religious wedding in the UK (eg Muslim, Sikh or Hindu) then it is very straight forward just to go the Registry Office and have a civil ceremony and you will then be married.
However, if you got married abroad then things are different. If you got married in a different country and a religious wedding is accepted in that country as a legal marriage then you are already married in the UK and you cannot register your marriage again.
"Would kids be charged inheritance tax?"
That all depends on how much your estate is worth and what is written in your will (if you have one).
If you do not have a will and your marriage is not recognised in this country then a jointly owned property (unless it's owned as tenants in common) will pass to your partner. The same applies to any jointly owned bank accounts etc.
Everything else in just your name will go to your children.
In this situation, IHT is payable on everything over the value of £325,000 in your estate. And that includes the half of your home that you own jointly with your partner. So both your partner and children could face having to deal with IHT depending on the total value of your estate.
If you were married abroad or you subsequently get married here then it increases how much you can leave without paying any IHT.
As a previous poster said "...a few friends who thought of marriage as an unnecessary piece of paper are having quick weddings for tax purposes."
I would strongly suggest that you write a will and also determine if you are already married in the UK.